Fractal Structures of General Mandelbrot Sets and Julia Sets Generated From Complex Non-Analytic Iteration Fm(Z)=Zm+c

DOI

10.2991/isccca.2013.42How to use a DOI?

Keywords

Complex Non-analytic Iteration, Critical Point, General Mandelbrot Set, Julia Set

Abstract

In this paper we use the same idea as the complex analytic dynamics to study general Mandelbrot sets and Julia sets generated from the complex non-analytic iteration . The definition of the general critical point is given, which is of vital importance to the complex non-analytic dynamics. The general Mandelbrot set is proved to be bounded, axial symmetry by real axis, and have (m+1)-fold rotational symmetry. The stability condition of periodic orbits and the boundary curve of stability region of one-cycle are given. And the general Mandelbrot sets are constructed by the escape-time method and the periodic scanning algorithm, which present a better understanding of the structure of the Mandelbrot sets. The filled-in Julia sets Km,c have m-fold structures. Similar to the complex analytic dynamics, the general Mandelbrot sets are kinds of mathematical dictionary or atlas that map out the behavior of the filled-in Julia sets for different values of c.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Dejun Yan
AU  - Xiaodan Wei
AU  - Hongpeng Zhang
AU  - Nan Jiang
AU  - Xiangdong Liu
PY  - 2013/02
DA  - 2013/02
TI  - Fractal Structures of General Mandelbrot Sets and Julia Sets Generated From Complex Non-Analytic Iteration Fm(Z)=Zm+c
BT  - Proceedings of the 2nd International Symposium on Computer, Communication, Control and Automation (ISCCCA 2013)
PB  - Atlantis Press
SP  - 167
EP  - 170
SN  - 1951-6851
UR  - https://doi.org/10.2991/isccca.2013.42
DO  - 10.2991/isccca.2013.42
ID  - Yan2013/02
ER  -